Back to Search
Start Over
So, what exactly is a qualitative calculus?
- Source :
-
Artificial Intelligence . Dec2020, Vol. 289, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- The paradigm of algebraic constraint-based reasoning, embodied in the notion of a qualitative calculus, is studied within two alternative frameworks. One framework defines a qualitative calculus as "a non-associative relation algebra (NA) with a qualitative representation", the other as "an algebra generated by jointly exhaustive and pairwise disjoint (JEPD) relations". These frameworks provide complementary perspectives: the first is intensional (axiom-based), whereas the second one is extensional (based on semantic structures). However, each definition admits calculi that lie beyond the scope of the other. Thus, a qualitatively representable NA may be incomplete or non-atomic, whereas an algebra generated by JEPD relations may have non-involutive converse and no identity element. The divergence of definitions creates a confusion around the notion of a qualitative calculus and makes the "what" question posed by Ligozat and Renz actual once again. Here we define the relation-type qualitative calculus unifying the intensional and extensional approaches. By introducing the notions of weak identity, inference completeness and Q-homomorphism, we give equivalent definitions of qualitative calculi both intensionally and extensionally. We show that "algebras generated by JEPD relations" and "qualitatively representable NAs" are embedded into the class of relation-type qualitative algebras. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00043702
- Volume :
- 289
- Database :
- Academic Search Index
- Journal :
- Artificial Intelligence
- Publication Type :
- Academic Journal
- Accession number :
- 146811134
- Full Text :
- https://doi.org/10.1016/j.artint.2020.103385